The Hovey–Strickland and Chai conjectures. Proves Chai's invariant-ideal conjecture for Lubin–Tate deformation rings over finite residue fields, at every prime and positive height n. Through the implication of Barthel–Heard–Naumann, this proves the Hovey–Strickland conjecture: dualizable $K(n)$-local spectra have exactly $n+2$ thick tensor ideals, and their Balmer spectrum is a chain of $n+1$ points.
released 2026-09-24 | 6 theorems · 13 lemmas · 27 proofs · 15,665 words |
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We classify the prime and radical ideals of the Lubin–Tate deformation ring invariant under an open Morava stabilizer subgroup, at every prime and positive height. This proves Chai's invariant-ideal conjecture in the standard finite-residue-field formulation. It also proves the Hovey–Strickland conjecture: the dualizable $K(n)$-local category has exactly $n+2$ thick tensor ideals, and its Balmer spectrum is a chain of $n+1$ points.